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Solve the inequality x/(x+2) ≤ 4/(x-3) for x ≠ -2 or 3

First we need to find the critical values. To find the critical values we must rearrange the equation and then replace the inequality symbol with an equals sign. The ≤ can be treated as an equality as long a...
GS
4395 Views

Calculate the value of the square root of 3 to four decimal places using the Newton-Raphson process

Newton-Raphson is used for finding a numerical solution to equations of the form f(x)=0. The question asks for the square root of 3, which algebraically looks like this: x = sqrt(3) This can be rewritten in ...
WS
7691 Views

What are the different forms of complex numbers and how do you convert between them?

Complex numbers have three primary forms: the general form, z=a+ib; the polar form, z=r(cosθ+isinθ); and the exponential form, z=rexp(iθ). To convert from the general form to either form you need to find r a...
PL
41516 Views

f(x) = 9x^3 – 33x^2 –55x – 25. Given that x = 5 is a solution of the equation f(x) = 0, use an algebraic method to solve f(x) = 0 completely.

x=5 is a solution, so (x-5) is a factor of f(x). So, to find the other solutions, factorise f(x): f(x)=(x-5)(ax^2+bx+c). We know it will be of this form because f(x) is cubic. To find the values of a, b and ...
PR
10613 Views

What is the general solution to the equation d2y/dx2 + dy/dx - 2y = -3sinx + cosx (d2y/dx2 signals a second order derivative)

The first step is to find the complementary function, yc, which is done by setting up a quadratic based upon the differential equation of the form m^2 + m -2 = 0 (i.e m^2 = d2y/dx2, m = dy/dx, and y is a con...
AS
9878 Views